Displacement (vector) in the context of Dead and live loads

Mechanics (from Ancient Greek μηχανική (mēkhanikḗ) 'of machines') is the area of physics concerned with the relationships between force, matter, and motion among physical objects. Forces applied to objects may result in displacements, which are changes of an object's position relative to its environment.

Theoretical expositions of this branch of physics have their origins in Ancient Greece, for instance, in the writings of Aristotle and Archimedes (see History of classical mechanics and Timeline of classical mechanics). During the early modern period, scientists such as Galileo Galilei, Johannes Kepler, Christiaan Huygens, and Isaac Newton laid the foundation for what is now known as classical mechanics.

In geometry, a position or position vector, also known as location vector or radius vector, is a Euclidean vector that represents a point P in space. Its length represents the distance in relation to an arbitrary reference origin O, and its direction represents the angular orientation with respect to given reference axes. Usually denoted x, r, or s, it corresponds to the straight line segment from O to P.In other words, it is the displacement or translation that maps the origin to P:

The term position vector is used mostly in the fields of differential geometry, mechanics and occasionally vector calculus.Frequently this is used in two-dimensional or three-dimensional space, but can be easily generalized to Euclidean spaces and affine spaces of any dimension.

In science, work is the energy transferred to or from an object via the application of force along a displacement. In its simplest form, for a constant force aligned with the direction of motion, the work equals the product of the force strength and the distance traveled. A force is said to do positive work if it has a component in the direction of the displacement of the point of application. A force does negative work if it has a component opposite to the direction of the displacement at the point of application of the force.

For example, when a ball is held above the ground and then dropped, the work done by the gravitational force on the ball as it falls is positive, and is equal to the weight of the ball (a force) multiplied by the distance to the ground (a displacement). If the ball is thrown upwards, the work done by the gravitational force is negative, and is equal to the weight multiplied by the displacement in the upwards direction.

The foot-pound force (symbol: ft⋅lbf, ft⋅lb_f, or ft⋅lb ) is a unit of work or energy in the engineering and gravitational systems in United States customary and imperial units of measure. It is the energy transferred upon applying a force of one pound-force (lbf) through a linear displacement of one foot. The corresponding SI unit is the joule, though in terms of energy, one joule is not equal to one foot-pound.

A structural load or structural action is a mechanical load (more generally a force) applied to structural elements. A load causes stress, deformation, displacement or acceleration in a structure. Structural analysis, a discipline in engineering, analyzes the effects of loads on structures and structural elements. Excess load may cause structural failure, so this should be considered and controlled during the design of a structure. Particular mechanical structures—such as aircraft, satellites, rockets, space stations, ships, and submarines—are subject to their own particular structural loads and actions. Engineers often evaluate structural loads based upon published regulations, contracts, or specifications. Accepted technical standards are used for acceptance testing and inspection.

Structural mechanics or mechanics of structures is the computation of deformations, deflections, and internal forces or stresses (stress equivalents) within structures, either for design or for performance evaluation of existing structures. It is one subset of structural analysis. Structural mechanics analysis needs input data such as structural loads, the structure's geometric representation and support conditions, and the materials' properties. Output quantities may include support reactions, stresses and displacements. Advanced structural mechanics may include the effects of stability and non-linear behaviors.

Mechanics of structures is a field of study within applied mechanics that investigates the behavior of structures under mechanical loads, such as bending of a beam, buckling of a column, torsion of a shaft, deflection of a thin shell, and vibration of a bridge.